SOLUTION: Hi Stuck on this question Express the following as a partial fraction 3x-1/x^2+4x+4 Really confuced here, i take it you factorise the equation to get 3x-1/(x+2)(x+2)

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Hi Stuck on this question Express the following as a partial fraction 3x-1/x^2+4x+4 Really confuced here, i take it you factorise the equation to get 3x-1/(x+2)(x+2)       Log On


   

Question 358027: Hi Stuck on this question
Express the following as a partial fraction
3x-1/x^2+4x+4
Really confuced here, i take it you factorise the equation to get
3x-1/(x+2)(x+2)

Thanks
Found 2 solutions by Fombitz, solver91311:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
%283x-1%29%2F%28x%5E2%2B4x%2B4%29=A%2F%28x%2B2%29%2BB%2F%28x%2B2%29%5E2
Multiplying by the denominator,
3x-1=A%28x%2B2%29%5E2%2BB
3x-1=A%28x%2B2%29%2BB
Ax%2B2A%2BB=3x-1
.
.
highlight%28A=3%29
.
.
2A%2BB=-1%7D%7D%0D%0A%7B%7B%7B2%283%29%2BB=-1
highlight%28B=-7%29

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


So far, so good. But when you decompose partial fractions, if you have a factor squared in the original denominator, you have to represent the single factor in one denominator and the squared factor in another one, thus:



Apply the LCD in the RHS:



Hence, equating the coefficients in the numerators:



And



Therefore:



John

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